Despite the discrimination of lossy channels has been already considered in
the literature, the approach of this paper is novel. Previous works have in
fact considered this kind of discrimination by constraining the energy
irradiated over the unknown lossy channel but not the total energy employed in
preparing the input states. For instance, in the quantum reading of digital
memories [1]}, the discrimination of lossy channels has been
analyzed by fixing the mean total number of photons irradiated over the
channel, independently on the number of probing modes (this approach has been
also followed by the recent Ref. [2]}). Previously, in the quantum
illumination of targets [3]}, [4]}, the channel
discrimination was performed by fixing the mean number of photons in each of
the modes probing the channel. In both these models there was no restriction
for the energy involved in the use of ancillary modes. Our approach considers
the discrimination of lossy channels by constraining the total energy of the
input state, thus including both the probing mode (irradiated over the unknown
lossy channel) and a possible ancillary mode (bypassing the lossy channel and
detected by the output measurement). Thus, while previous models were more
focussed on restricting the energy irradiated over the channel, we address the
problem from the point of view of the input source, i.e., considering the
global effort in preparing this source. By fixing the input energy, we then
optimize over an important class of Gaussian states, i.e., single- and
two-mode squeezed thermal states. The choice of these states relies in their
experimental accessibility, being routinely generated in today's quantum
optics laboratories where they can be reliably controlled [5]}.
Furthermore, because of the squeezing, they represent important examples of
non-classical states, i.e., states with non-positive P representation
[6]}. This is another feature which diversifies our study from
previous works [1]}, [3]}, where the main goal was the
comparison between non-classical states and classical states (i.e., with
positive P representation). Note also that our problem, involving a discrete
channel discrimination, is completely different from problems of parameter
estimation, where one has to infer a parameter taking continuous values. The
estimation of the damping constant of a bosonic channel has been recently
addressed by Refs. [9]}, [10]}, [11]}, [12]}.
